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The following are the details of the wire I have:

Nichrom 80, 32 Gauge (0.2744 mm diameter), measured resistance 6.84 ohms/foot or 22.44 ohms/m.

I'm planning on powering this only via USB so my max power would be 2.4 amps, and voltage would be 5 V.

I don't really care about how much temperature is lost to its surroundings, even if the wire reaches ±10 degrees I'm happy. If time is a factor, I would like for it to heat up to this much within an hour if possible.

Since it is important, lets say the ambient temperature is 25°C and that I'm enclosing the wire in an insulated box of 100 cm3 so that the room's temperature eventually has negligible effect on the temperature of the wire

How would I go about calculating the length of wire needed for the task based on these parameters?

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    \$\begingroup\$ a 70 °C hand warmer runs a serious risk of giving the wearer first-degree burns. Are you sure you want 70 °C? \$\endgroup\$
    – Hearth
    Dec 5, 2023 at 16:28
  • \$\begingroup\$ There is no length of nichrome wire that would guarantee a maximum of 70 °C. 70 °C may cause not only first degree burns. It is not possible to calculate a length based on your parameters. \$\endgroup\$
    – Uwe
    Dec 5, 2023 at 16:45
  • \$\begingroup\$ I'm going to put it inside a thick silicone sheet, which is why i was aiming for 70 \$\endgroup\$ Dec 5, 2023 at 17:07
  • \$\begingroup\$ Silicone will be fairly good insulator, I suspect. \$\endgroup\$
    – Transistor
    Dec 5, 2023 at 17:54

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Temperature of the wire will be dominated by the balance of heat loss to heat input. It is therefore almost impossible to answer your question without providing more details on the environment round the wire (conductivity, ambient temperature, etc.).

For instance, if the element was in a large bath of cold insulating liquid, 2.4A over a few inches length would likely lead to minimal temperature increase in the wire. If the wire was in a hard vacuum, you might well be able to melt it.

What you can say, is that maximum heat will be generated when the resistance is around 2Ω, as this will give about 2.5A at 5V, for around 12.5W. The maximum power will therefore be with about 3.5" of wire (based on your 6.8Ω/ft).

Shorter wire lengths will overload your supply (as current will be above 2.5A). Longer lengths will reduce both total power, and also the power per unit length.

Depending on your application, it may be that multiple longer lengths in parallel (giving 2Ω total resistance) will give you a more even heat distribution. The lower linear power density will definitely reduce the risk of extremely high localized heating.

You also need to decide if you actually care about wire temperature, or if it is the temperature of the environment you wish to be at 70°C.

In general, the higher the linear power density, the larger the difference between the wire temp and the surrounding temperature (as wire-ambient thermal resistance will be relatively stable). Again this means that if you want a stable setup, with low wire temperature, multiple parallel strands might be your best bet.

Lower linear densities will also tend to give you more stable control if you decide to add feedback and an active control loop.

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    \$\begingroup\$ knowing ambient temp is also necessary. Starting at \$30^\circ\$ C is very different from starting at zero \$\endgroup\$ Dec 5, 2023 at 14:11
  • \$\begingroup\$ ok say the ambient temperature is 25 degrees. and that I'm enclosing the wire in an insulated box of 100 cm3 so that the rooms temperature eventually has negligible effect on the temperature. \$\endgroup\$ Dec 5, 2023 at 14:24
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    \$\begingroup\$ Some very rough rule-of-thumb figures: 1 kW into 1 m³ will cause a temperature rise of 1°C/s. Can you do the maths with that information? \$\endgroup\$
    – Transistor
    Dec 5, 2023 at 14:27
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    \$\begingroup\$ By 100 cm3, do you mean a box 100cm each side and volume 1m3, or a a box 4.6cm each side, volume 100cm3? \$\endgroup\$
    – colintd
    Dec 5, 2023 at 15:11
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    \$\begingroup\$ @Transistor You can also use the Unicode symbols Ω, μ, °, and so on, in both posts and comments. Having xcompose or wincompose set up properly is convenient. \$\endgroup\$
    – Hearth
    Dec 5, 2023 at 15:38

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